Acceleration of expanding universe question

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SUMMARY

The discussion centers on the acceleration of the universe's expansion, specifically addressing how astronomers determine that galaxies are currently accelerating rather than having done so in the distant past. By observing galaxies at various distances, which correspond to different points in time, researchers can compare current velocities with those from approximately 13 billion years ago. This method allows for the extrapolation of current velocities of distant galaxies based on the observed velocities of nearby galaxies.

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If we are looking further and further back in time when we look at more and more distant galaxies, then how do we know that they are accelerating (instead of that they were accelerating a long long time ago)??
 
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You can look at galaxies everywhere from "now" to ~13 billion years ago. This allows to get the current velocities as well as the velocities in the past.
You don't see the same galaxies as they are now and as they were 13 billion years ago, of course, but if you see the current velocity of galaxies nearby you can extrapolate this to get the current velocity of more distant galaxies.
 

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